Multiply and simplify the following complex numbers: $({-3+2i}) \cdot ({1-i})$
Solution: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-3+2i}) \cdot ({1-i}) = $ $ ({-3} \cdot {1}) + ({-3} \cdot {-i}) + ({2i} \cdot {1}) + ({2i} \cdot {-i}) $ Then simplify the terms: $ (-3) + (3i) + (2i) + (-2i^2) $ Imaginary unit multiples can be grouped together. $ -3 + (3 + 2)i - 2 i^2 $ After we plug in $i^2 = -1$, the result becomes $ -3 + (3 + 2)i - (-2) $ The result is simplified: $ (-3 + 2) + (5i) = -1+5i $